Space of modular forms of level 240 and weight 3

• Label: 240.3
• Level: 240
• Weight: 3
• Dimension: 1162
• Nonzero newspaces: 14
• Newform subspaces: 31
• Sturm bound: 9216
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 14 \)
Newform subspaces:			\( 31 \)
Sturm bound:			\(9216\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(240))\).

	Total	New	Old
Modular forms	3296	1214	2082
Cusp forms	2848	1162	1686
Eisenstein series	448	52	396

Trace form

1162 * q - 4 * q^3 - 32 * q^4 - 12 * q^5 - 24 * q^6 - 32 * q^7 + 24 * q^8 + 18 * q^9 + 64 * q^10 - 64 * q^11 + 104 * q^12 + 88 * q^14 - 18 * q^15 - 64 * q^16 - 8 * q^17 + 88 * q^18 + 188 * q^19 - 80 * q^20 + 64 * q^21 - 160 * q^22 + 352 * q^23 + 32 * q^24 + 34 * q^25 + 200 * q^26 + 44 * q^27 + 240 * q^28 + 56 * q^29 + 124 * q^30 - 60 * q^31 + 240 * q^32 - 8 * q^33 + 160 * q^34 - 384 * q^36 + 208 * q^37 - 224 * q^38 + 176 * q^39 - 312 * q^40 + 88 * q^41 - 688 * q^42 - 40 * q^43 - 736 * q^44 - 32 * q^45 - 800 * q^46 - 192 * q^47 - 520 * q^48 - 694 * q^49 - 544 * q^50 - 172 * q^51 - 112 * q^52 + 168 * q^53 + 320 * q^54 + 80 * q^55 + 448 * q^56 + 144 * q^57 + 832 * q^58 + 256 * q^59 + 512 * q^60 + 572 * q^61 + 552 * q^62 + 160 * q^63 + 544 * q^64 + 312 * q^65 + 152 * q^66 + 792 * q^67 - 336 * q^68 - 36 * q^69 - 1240 * q^70 + 256 * q^71 - 344 * q^72 - 616 * q^73 - 1576 * q^74 - 72 * q^75 - 2112 * q^76 - 928 * q^77 - 1456 * q^78 - 764 * q^79 - 392 * q^80 - 38 * q^81 - 992 * q^82 - 864 * q^83 - 1152 * q^84 - 1148 * q^85 - 160 * q^86 - 1240 * q^87 - 96 * q^88 - 696 * q^89 + 328 * q^90 - 2656 * q^91 + 880 * q^92 - 464 * q^93 + 1712 * q^94 - 2112 * q^95 + 1056 * q^96 - 56 * q^97 + 1792 * q^98 - 456 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(240))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
240.3.c	\(\chi_{240}(209, \cdot)\)	240.3.c.a	1	1
		240.3.c.b	1
		240.3.c.c	4
		240.3.c.d	4
		240.3.c.e	12
240.3.e	\(\chi_{240}(31, \cdot)\)	240.3.e.a	4	1
		240.3.e.b	4
240.3.g	\(\chi_{240}(151, \cdot)\)	None	0	1
240.3.i	\(\chi_{240}(89, \cdot)\)	None	0	1
240.3.j	\(\chi_{240}(79, \cdot)\)	240.3.j.a	4	1
		240.3.j.b	4
		240.3.j.c	4
240.3.l	\(\chi_{240}(161, \cdot)\)	240.3.l.a	2	1
		240.3.l.b	2
		240.3.l.c	4
		240.3.l.d	8
240.3.n	\(\chi_{240}(41, \cdot)\)	None	0	1
240.3.p	\(\chi_{240}(199, \cdot)\)	None	0	1
240.3.q	\(\chi_{240}(19, \cdot)\)	240.3.q.a	96	2
240.3.r	\(\chi_{240}(101, \cdot)\)	240.3.r.a	128	2
240.3.u	\(\chi_{240}(23, \cdot)\)	None	0	2
240.3.x	\(\chi_{240}(73, \cdot)\)	None	0	2
240.3.z	\(\chi_{240}(83, \cdot)\)	240.3.z.a	184	2
240.3.ba	\(\chi_{240}(13, \cdot)\)	240.3.ba.a	96	2
240.3.bd	\(\chi_{240}(203, \cdot)\)	240.3.bd.a	184	2
240.3.be	\(\chi_{240}(133, \cdot)\)	240.3.be.a	96	2
240.3.bg	\(\chi_{240}(97, \cdot)\)	240.3.bg.a	4	2
		240.3.bg.b	4
		240.3.bg.c	4
		240.3.bg.d	4
		240.3.bg.e	8
240.3.bj	\(\chi_{240}(47, \cdot)\)	240.3.bj.a	8	2
		240.3.bj.b	16
		240.3.bj.c	24
240.3.bm	\(\chi_{240}(29, \cdot)\)	240.3.bm.a	8	2
		240.3.bm.b	176
240.3.bn	\(\chi_{240}(91, \cdot)\)	240.3.bn.a	64	2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(240)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)